Lecture Notes on 03 Oct 2011

// Get the largest gap between palindromic years
intialize maxGap to 0
initialize begYear to 0
intialize endYear to 0
intialize lastPalYear to 0
intialize gap to 0
loop year from 1 to 2011 inclusive
  if year is palindromic
    set gap = year - lastPalYear
    if gap is greater than maxGap then
      set maxGap to gap
      set begYear to lastPalYear
      set endYear to year
    end if
    set lastPalYear to year
  end if
end loop
print maxGap
print begYear and endYear


// get two digit number that becomes palindromic with maximum number of steps
initialize maxSteps to 0
initialize maxNum to 0
initialize steps to 0
loop num from 10 to 99 inclusive
  initialize revSum to num
  set steps to 0
  while revSum is not palindromic do
    increment steps
    set revSum = revSum + reverse of revSum
  end while
  if steps is greater than maxSteps then
    set maxSteps = steps
    set maxNum = num
  end if
end loop
print maxNum
print maxSteps


public class Quiz4
{
  public static long revNum (long n)
  {
    long rev_num = 0;
    while (n > 0)
    {
      rev_num = rev_num * 10  + (n % 10);
      n = n / 10;
    }
    return rev_num;
  }

  public static boolean isPalindromic (long n)
  {
    return (n == revNum(n)); 
  }

  public static void main (String[] args)
  {
    // biggest gap between palindromic years
    int max_gap = 0;
    int beg_year = 0;
    int end_year = 0;
    int last_pal_year = 0;
    int gap = 0;
    for (int year = 1; year <= 2011; year++)
    {
      if (isPalindromic (year))
      {
        gap = year - last_pal_year;
	if (gap >= max_gap)
	{
          max_gap = gap;
	  beg_year = last_pal_year;
	  end_year = year;
	}
	last_pal_year = year;
      }
    }
    System.out.println ("The largest gap was: " + max_gap);
    System.out.println ("The years were: " + beg_year + ", " + end_year);

    // palindromic sum
    long max_num = 0;
    long max_steps = 0;
    long steps = 0;
    for (long num = 10; num <= 99; num++)
    {
      long sum_num = num;
      steps = 0;
      while (!isPalindromic(sum_num))
      {
        steps++;
	sum_num = sum_num + revNum (sum_num);
      }
      if (steps > max_steps)
      {
        max_steps = steps;
	max_num = num;
      }
    }
    System.out.println ("The number is: "+ max_num);
    System.out.println ("The number of steps is: " + max_steps);
  }
}